Another way of looking at it.. ..Think only of the lowest point of the tangent arc. Crystals along the dotted red curve between the lamp and the eye will glint the lamplight towards the eye.

Crystals near the eye form overlapping halos that make the trumpet shape.

The trumpet shapes are divergent light halo versions of the well known upper tangent arc.

The sun produced tangent arc touches the uppermost point of the 22° halo. Horizontal column crystals make it.

The divergent light tangent arc's lowest point similarly touches the uppermost edge of Minnaert's cigar. The halo's other rays originate from a complex caustic surface winging outwards above it. The surface is shown as blue and green in the diagram at left with Minnaert's cigar greyed out below it. A horizontal column crystal anywhere on this surface contributes to the edge of the tangent arc. The precise shape of the caustic surface depends on the elevation of the lamp relative to the eye - remember how the sun-made tangent arc changes with solar altitude.

The trumpet shapes seen here are mainly from the caustic surface relatively close to the eye.

Tangent Arc from divergent light. Horizontal column crystals on the complex blue and green surface form the halo. The surface is attached to the top of Minnaert's cigar.

Divergent light halos
Ordinary halos around the sun or moon come from parallel light. Street lamps and other lights form halos but they are more exotic for the light forming them is divergent. When the light is comparatively nearby the halos take on a weirdly 3D aspect.

The divergent light “22 degree halo” is maybe the easiest to understand. Rays from the lamp deviated by 22 degrees form the halo’s inner edge. The crystals that do this are on an elongated caustic surface stretching from the lamp to the eye called “Minnaert’s Cigar”. Crystals inside the caustic send no light to the eye, those slightly outside it form the outer fuzzy regions of the halo. The divergent light halo is smaller than the 22° halo around the sun.

Minnaert's Cigar named after atmospheric optics pioneer Marcel Minnaert. Crystals at the surface deviate light through 22° to form a divergent light circular halo.